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Optimal approximation of sparse Hessians and its equivalence to a graph coloring problem. (English) Zbl 0507.65027

MSC:
65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
65F50 Computational methods for sparse matrices
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[1] J.A. Bondy and U.S.R. Murty,Graph theory with applications (MacMillan, London, 1976). · Zbl 1226.05083
[2] T.F. Coleman and J.J. MorĂ©, ”Estimation of sparse Jacobian matrices and graph coloring problems”, Technical Report ANL-81-39, Argonne National Laboratory (Argonne, IL, 1981). · Zbl 0527.65033
[3] A.R. Curtis, M.J.D. Powell and J.K. Reid, ”On the estimation of sparse Jacobian matrices”,Journal of the Institute of Mathematics and its Applications 13 (1974) 117–119. · Zbl 0273.65036
[4] M.R. Garey and D.S. Johnson,Computers and intractability (Freeman San Francisco, CA, 1979). · Zbl 0411.68039
[5] G.R. Grimmet and C.J.H. McDiarmid, ”On colouring random graphs”,Proceedings of the Cambridge Philosophical Society 77 (1975) 313–324. · Zbl 0297.05112
[6] D.S. Johnson, ”Worst case behavior of graph coloring algorithms”. in:Proceedings of the 5th Southeastern Conference on Combinatorics, Graph Theory, and Computing (Utilitas Mathematica, Winnipeg. Man., 1974) pp. 513–527. · Zbl 0308.05109
[7] R.M. Karp, ”Reducibility among combinatorial problems” in: R.E. Miller and J.W. Thatcher, eds.,Complexity of computer computations (Plenum, New York, 1972) pp. 85–103.
[8] M.J.D. Powell and P.L. Toint, ”On the estimation of sparse Hessian matrices”,SIAM Journal on Numerical Analysis 16 (1979), 1060–1074. · Zbl 0426.65025
[9] M.N. Thapa, ”Optimization of unconstrained functions with sparse Hessian matrices”, Ph.D. Thesis, Stanford University (Stanford, CA, 1980).
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